# Questions tagged [lagrangian-relaxation]

For questions related to Lagrangian relaxation, a method used to generate bounds on optimization problems by removing one or more constraints and including a penalty in the objective function for violating the removed constraints.

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### Lagrangian Relaxation Lower Bound exceeds the Upper bound and the Optimal solution

I'm trying to minimize an MIP model employing a Lagrangian relaxation approach. However, I've encountered an issue where, in certain instances, the lower bound (resulting from the Lagrangian sub-...
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### Lagrange relaxation / subgaradient algorithm Sensivity to input data

I am implementing a Lagarange relaxation with subgradient method to find a lower bound for a minization problem, I tried to find the complicating constraints. I found an upper bound with relatively ...
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### Finding lower bound (maximization problem) in Lagrangian Relaxation with subgradient method

I have tried to implement a toy problem (MIP) from the literature using Lagrangian Relaxation with the subgradient method, I implemented it correctly and I got the upper bound which is updated at each ...
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1 vote
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### Combination of lagrangian relaxation and column generation

I am solving an integrated scheduling problem and have dealt with coupling constraints using Lagrangian relaxation to decompose the problem into two separate problems. However, it is still difficult ...
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### Partial Lagrangian in the Max-Flow problem

In the question: "Partial" Lagrangian Dual in LP It is argued that considering a partial Lagrangian $L_{partial}$, where we Dualize only some of the constraints, results in a tighter ...
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### Lagrangian Relaxation The Weak Lower Bound

I am applying Lagrangian Relaxation with Subgradient Optimization Method and trying to solve a MIP model. Before testing the large-scale instances, I wanted to see how it performs on small-size ones. ...
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### Using LR-based method to solve mixed integer programming

When we use Lagrangian relaxation-based methods to solve mixed integer programming, does the convergence of multipliers to the optimum as well as convergence of primal variables to the optimum happen ...
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### Lagrangian Relaxation bound greater than optimal solution

I am working on a Lagrangian relaxation for a minimization MIP. Everything seemed to be working fine before I started to run a batch of instances. Checking the log results for one of the instances ...
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### How to Speed Up the subgradient optimization procedure in a Lagrangian Relaxation Scheme

I'm currently working on the following problem (a variant of maximal k-covering problem): \begin{align} \max&\quad z =\sum\limits_{\omega\in \Omega}x_{\omega} \label{imbip3a} \\ \text{s.t.}&\...
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### Difficulties with Finding a Proper Penalty Value for the Progressive Hedging Algorithm

Recently, I've been working on some two-stage stochastic programming problems. Due to the presence of integer second-stage variables in the model, I've preferred to use the Progressive Hedging ...
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